Hi,
Probation period can be extended only through a formal order on or before the expiry of the probation. If not, the prescribed probation period automatically is considered to have been completed successfully.
So far as the other part of your question, you have not mentioned whether it is a Limited Company, Private Limited Company or a totally private firm. However, if you have signed any agreement before employment, there could be a mention of notice period for termination of employment in your agreement. You may check that and can claim salary in lieu of the notice period.
If in your appointment letter it has been written that your services could be terminated without notice or without quoting any reason, although that is illegal under the provisions of notice period of the Industrial Disputes Act or the Shops and Establishment Act of the State, you may have to struggle hard to make a claim, as you have already accepted that term before joining duty. However, you are free to go to the labor court or a civil court, as the case may be, to prefer your claim for the illegality on the part of your employer. If it is a private firm, you can approach to the Inspector of Shops and Establishment of your state to bring before him the violation of provisions of shops and establishment act. So, at first, you may need to check the language of your appointment before deciding any course of action against the management of he organization.
About payment of Gratuity, as per Section 4(1) & 4(2) of the Payment of Gratuity Act, 1972, if you have rendered service of NOT LESS THAN 5 years, for every completed year of service or part thereof in excess of six months, the employer is liable to pay gratuity to you at the rate of fifteen days wages based on the rate of wages last drawn by you: